The Poland international netted twice, while Marco Reus also found the back of the net, as last year's runner-up kick-started their European campaign
Robert Lewandowski, who netted a double, and Marco Reus were the men on target as the hosts - beaten finalists last term - got their first-ever win in the competition against the French side.
Poland international Lewandowski put the finishing touches to a well-worked team goal after 19 minutes before Reus' free-kick found its way into the back of the net seven minutes after the break.
Lewandowski then added a third from the spot late on to wrap up the victory.
The home side - who were watched by coach Jurgen Klopp from the stands as he served a one-match touchline ban for his protests in the defeat against Napoli - were without goalkeeper Roman Weidenfeller following a red card in the Group F opener, while Eric Durm replaced the injured Marcel Schmelzer.
Marseille were once again without striker Andre-Pierre Gignac, who has been sidelined with a toe injury.
Both sides came into the game off the back of domestic wins at the weekend – against Lorient and Freiburg respectively - but it was Dortmund who began the brighter, with Reus firing narrowly over in the second minute before forcing a save from Steve Mandanda.
However, Marseille had strong claims for a penalty turned down shortly afterwards when Saber Khelifa went down under a challenge from Durm.
Dortmund eventually went ahead through a goal of the highest quality after 18 minutes, with Lewandowski netting his third goal in four days.
After a quick break, Reus played in Henrikh Mkhitaryan. He fired across goal to Durm, who in turn put the ball on a plate for the Pole to cap off a wonderfully worked team goal.
While Dortmund continued to enjoy plenty of possession, they struggled to create too many further clear-cut chances before the break.
However, they were two goals ahead six minutes after the interval after a Reus free-kick forced Mandanda into a costly error.
The visitors' goalkeeper flapped at the inswinging delivery and, while he tried desperately to claw the ball out, his efforts proved futile as the ball crept in and Dortmund doubled their lead.
Mandanda then went some way to atoning for his error, producing a smart stop to deny Durm from close range after 58 minutes.
But Lewandowski made it three 10 minutes from time from the penalty spot after Reus had been pulled down by Khelifa in the area to cap off a comfortable victory for Klopp's men.